White dwarf stars in D dimensions

We derive the mass-radius relation of relativistic white dwarf stars (modeled as a self-gravitating degenerate Fermi gas at T=0) in a D-dimensional universe and study the influence of the dimension of space on the laws of physics when we combine quantum mechanics, special relativity, and gravity. We exhibit characteristic dimensions D=1, D=2, D=3, D=(3+root 17)/2, D=4, D=2(1+root 2) and show that quantum mechanics cannot balance gravitational collapse for D >= 4. This is similar to a result found by Ehrenfest (1917) at the atomic level for Coulomb forces (in Bohr's model) and for the Kepler problem. This makes the dimension of our universe D=3 very particular with possible implications regarding the anthropic principle. We discuss some historic aspects concerning the discovery of the Chandrasekhar (1931) limiting mass in relation to previous investigations by Anderson (1929) and Stoner (1930). We also propose different derivations of the stability limits of polytropic distributions and consider their application to classical and relativistic white dwarf stars.